Infrared target detection technology has the advantages of large observation range, short scanning period and strong anti-interference ability, which is of great significance in space-based early warning missions. The infrared targets in space-based early warning missions have the characteristics of small size and weak signal, and it is difficult to use their texture and shape features for detection. In scenes with strong noise and clutter interference, it is necessary to use target motion features for detection. The traditional target detection algorithm generally assumes that targets move with constant velocity, which is not capable of detecting high dynamic nonlinear moving targets with unknown motion rules, and effective detection algorithms for nonlinear moving targets still need further development. To solve the problem of high dynamic and nonlinear moving target detection in space-based early warning missions, an infrared dim and small target detection algorithm based on LSTM is proposed.Firstly, an adaptive preprocessing block is proposed, which can extract the location information of suspicious targets and solves the problem of mismatch between LSTM network structure and sequence images. At the same time, some spatial characteristics of target signals are discarded in order to reduce the amount of computation. Then, due to the problem that traditional algorithms are unable to detect nonlinear motion trajectory, a target trajectory detection method based on LSTM is designed to realize the detection of high dynamic nonlinear moving targets in sequence images. Finally, a post-processing algorithm, which selects target points from the pre-processing results based on the LSTM estimation results is designed to improve the target positioning accuracy.Aiming at the targets with different motion laws, two experiments are designed and carried out based on the image sequence with an average signal-to-noise ratio of 4.07. In the first experiment, the target performs simple nonlinear motion with a sinusoidal law. This experiment proves that the proposed algorithm can correctly estimate the existence and position coordinates of the target with a precision rate of 0.934 7 and a recall rate of 0.885 1 (Fig.6-7). In the second experiment, the target performs complex nonlinear motion described by the superposition of multiple sine functions, the proposed algorithm achieves a precision rate of 0.936 2 and a recall rate of 0.863 3 at a detection speed of 0.008 326 s/frame and a peak memory usage of 1 214.13 MiB (Tab.2). Compared with four algorithms including Sequential Hypothesis Testing, the proposed algorithm is proved to have better performance in terms of precision rate, recall rate and detection speed. Through some additional experiments, it is proved that the algorithm is applicable to the detection task in the scenes where the average speed of target is between 1-6 pixels/frame and the average SCR and SNR of sequence images are both higher than 2.Experiments results demonstrate that the proposed algorithm has the ability to detect dim and small targets with high dynamic nonlinear motion from noise and clutter. The proposed algorithm makes use of the spatial and temporal features of the target in the sequence images, and is able to detect targets in low signal-to-noise ratio scenes. And at the same time, with the help of LSTM's ability to extract temporal features, the proposed algorithm is capable in the task of nonlinear moving targets detection. In addition, as the lightweight structure of the LSTM is maintained, the proposed algorithm shows high real-time performance.